Grassroots organisations such as Momentum and some of the biggest trade unions are preparing for a new leadership campaign in defence of Jeremy Corbyn after an overwhelming vote of no confidence from Labour MPs.

Momentum, set up after Corbyn’s victory last September to build on the enthusiasm generated during his campaign, held rallies in Newcastle, Leeds and Bristol on Tuesday after the vote. Thousands had demonstrated outside parliament on Monday night.

Corbyn has a strong chance of fending off a challenge if he can retain the support of the unions and the loyalty of the hundreds of thousands of members. He won in September with 59.5% of the vote.

MPs seeking to remove him are hoping much of that support has been eroded by discontent with his performances against David Cameron at prime minister’s questions, by scepticism over his ability to win a general election and by his lacklustre campaign in support of remain in the European Union referendum.

They also hope that by fielding just one candidate against him rather than three they stand a better chance of removing him.

Crucially for Corbyn, one of the biggest unions, Unite, has thrown its weight behind him. Shrugging off speculation that Unite’s support for him was wavering, Len McCluskey confirmed his continued support for the Labour leader. “The extraordinary behaviour of Labour MPs has achieved nothing beyond diverting attention from a Tory government in crisis,” McCluskey said.

“If anyone wants to change the Labour leadership, they must do it openly and democratically through an election, not through resignations and pointless posturing. If there has to be such an election, Jeremy Corbyn’s supporters throughout the movement will be ready for it.”

Jeremy Corbyn with Len McCluskey at a steelworkers’ march in London in May. Photograph: Leon Neal/AFP/Getty

The unions played a crucial role in the previous Labour leadership election, providing the financial backing as well as contributing activists to organise campaign events and staff phone banks.

Manuel Cortes, the general secretary of the Transport Salaried Staffs’ Association, also backed Corbyn. “It is almost unbelievable to watch the Labour party plunge into a crisis of its own making as its MPs involve themselves in childish, self-indulgent behaviour which doesn’t befit their office,” he said.

James Schneider, a spokesman for Momentum, which claims to have up to 100,000 members, said: “I think an enormous part of the Labour party membership and the Labour movement will be upset, disappointed and angry at the parliamentary Labour party’s vote.”

He added: “The grassroots of the Labour movement, including Momentum, are gearing up to support the leadership they elected.”

Ross Quinn, a spokesman for Momentum on Merseyside, which was holding an emergency meeting on Tuesday night in Liverpool, said they had been expecting the challenge since the day Corbyn had been elected but were confident of the outcome.

“Last year, we had to start from nothing. This time we have lots of people in place. We expect to repeat or do better than the numbers last year,” Quinn said.

A snap survey of Guardian readers, started on Monday, suggested that Corbyn still enjoys a large amount of support among party members in spite of reservations about his performance since becoming leader. The survey, to which more than 4,000 people responded (88% of them Labour members), is not scientific but does offer a large pool of opinions.

Even allowing for the likelihood that a disproportionate number of Corbyn supporters would have responded, there is much anger at the sniping against him by the parliamentary Labour party since the day he became leader.

The survey, conducted by the Guardian community team, asked readers a series of questions including whether they had voted for Corbyn last year, whether they planned to vote for him again, how they felt about his performance, and how they voted in last week’s European referendum.

Almost 90%of those who responded voted remain in the referendum in line with Labour’s position.

Of the respondents, 81% voted for Corbyn last year.Of those who voted for him last year, 95% continue to support him as party leader and said they were intending to vote for him again.

Vicky Ratcliffe, 37, a Labour member from London, said she would not be voting for Corbyn and expressed unhappiness over the referendum campaign. She said she did not vote for Corbyn last time but had been prepared to give him a chance to prove her wrong, but he did not. “His participation in the remain campaign was reluctant at best, and obstinate sabotage at the worst,” she wrote.

Ratcliffe, a community engagement specialist, added: “We need new blood. Young blood. The passion we have seen the Scottish National party develop north of the border. A British Justin Trudeau if possible.”

Among Corbyn supporters, Ros Sunley, 59, from Dorset, who is self-employed and intends to vote for him again, wrote: “I fully support Jeremy Corbyn and I am disgusted and appalled at the attitude and behaviour of those MPs who have set up the coup against him.”

Paddy Denning, 45, a teacher from Darlington, wrote: “I would not support any other candidate – but particularly important is that those who have publicly briefed against or undermined an elected leader should never serve the party again in any capacity, not even as MPs.

“We held off on deselections because Jeremy asked members to do so. This failed coup is a declaration of an anti-democratic war on the party membership.”